Path integral and noncommutative poisson brackets
P. Valtancoli
TL;DR
This paper explores how noncommutative Poisson brackets alter the relationship between Lagrangian and Hamiltonian formalisms, using path integral methods and applying findings to a harmonic oscillator with minimal length.
Contribution
It introduces a modified relation between Lagrangian and Hamiltonian frameworks in noncommutative settings using path integral formalism.
Findings
Noncommutative Poisson brackets modify the Lagrangian-Hamiltonian relation.
Path integral formalism is effective for analyzing noncommutative systems.
Application to harmonic oscillator reveals effects of minimal length.
Abstract
We find that in presence of noncommutative poisson brackets the relation between Lagrangian and Hamiltonian is modified. We discuss this property by using the path integral formalism for non-relativistic systems. We apply this procedure to the harmonic oscillator with a minimal length.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Noncommutative and Quantum Gravity Theories · Quantum Mechanics and Applications